¹ Other additional types of resistance are:

• ▪

  ▪ The appendage resistance (the drag caused by all the underwater appendages, such as the propeller, propeller shaft, struts, rudder, bilge keel and sea chest);

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  ▪ The steering resistance (the resistance caused by the motion of the rudder);

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  ▪ The wind and current resistance (wind and current are two of the biggest environmental factors affecting the ship);

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  ▪ The added resistance due to waves (refers to ocean waves caused by wind and storms, and it is not to be confused with wave making resistance);

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  ▪ The increase of resistance if the ship is in shallow water.

² Over the years a great number of empirical rules have been presented to the naval architects, rules which illustrate them with the aim of obtaining optimum hull forms. It is to be realized, however, that the wave-resistance theory provides the only method by which wave cancellation can be studied in a rational way.

³ There are noted examples of bulb refits on ships where the bulbs have actually performed worse than the bulb replaced, because the fact that bigger bulbs are better was assumed (see for example web page http://www.jjma.com/Documents/Services/NavalArchitecture/Hull_Form/cfd/CFD_Pages/bow.htm).

⁴ A remnant from the “ram bows” configurations of early steam warships of the late 1800's and even those of early Greek and Roman warships could be considered early versions of the bulbous bow even though their bow designs were intended for other purposes.

⁵ Admiral David Watson Taylor, USN (1864–1940) was a naval architect and engineer of the United States Navy. He served during the First World War as Chief Constructor of the Navy, and Chief of the Construction and Repair Bureau. Taylor is best known as the man who designed and built the first experimental towing tank ever built in the United States.

⁶ Weimblum, G., “Theorie des Wultschiffe”. Schiffbau Bd.37. 1936.

⁷ Wigley, W.C.S., “The Theory of Bulbous Bow and its Practical Application”, Transac. NECIES, Vol. 52, pp. 1935–1936.

⁸ Havelock, T.H., “The Wave Pattern of a Doublet in a Stream”, Collected Papers of Sir Thomas Havelock on Hydrodynamics. C. Wigley Editor of Naval Research. Department of the Navy, 1963.

⁹ Taylor, D.W., “Influence of the Bulbous Bow on Resistance”. Marine Engineering and Shipping Age. September 1923.

¹⁰ A Naval Architect, Professor Emeritus at Tokyo University. He showed that the bulbous bow not only benefits fine lined hulls at speeds in excess of about 18 knots –as it was initially thought–, but they also reduce the resistance of large full-bodied hulls moving at relatively slow speeds. They have since then become standard to large bulk carriers and tankers, even though these move at speeds where wave making resistance is a relatively small component (about 20%) of the overall resistance.

¹¹ Derived from these investigations, the first merchant ship with a bulbous bow was the “Yamashiro Maru” delivered in November, 1963 by a Japanese shipyard, which created quite a sensation in the European and American shipping world when it was first introduced.

¹² Since then, experimentation and refinement slowly improved the geometry of the bulbous bow, but they were not widely exploited until computer modelling techniques enabled researchers to increase their performance to a practical level in the 1980's, although for maximum benefit, model testing is still required to refine the proportions upon the hull form.

¹³ Eckert, E., Sarma, S.D., “Bow bulbs for Slow, Full-Form Ships”. SNAME. Technical and Research Bulletin pp. 1–33. New York, 1973.

¹⁴ Baba, E., “A New Component of Viscous Resistance of Ships”. Journal of Zosen Kiokai, n° 125, 1969.

¹⁵ Tupper, Eric C. Introduction to Naval Architecture, 4th. ed. Witherby & Co. Ltd., Oxford 2004, p. 168.

¹⁶ This is the reason why most warships cannot take full advantage of the bulbous bow since each bulb is generally “tuned” to the expected operating speed of the ship; an easy task for a merchant ship which usually operates at a constant speed between ports, but not for most warships whose tactical operations usually require continuous speed changes. On the contrary, many merchant ships operate at a steady speed during almost their whole lives, so the bulb can be designed for that speed.

¹⁷ The amplitude of the bulb wave mainly depends on the immersion of the bulb, while the phase depends on its protruding length.

¹⁸ For example, if we consider a 50,000 dwt cargo ship moving at 8 m/s (=15·6 knots), then the waves generated by the hull will also be moving at 8 m/s and so, from the wave theory equation where v is the speed of waves in m/s and λ the wavelength in m, the wavelength in this case would be 41 m, and consequently the bulb should be about 20 m ahead of the main bow wave source and so, this is likely to be about 10 m forward of the bow's intersection with the waterline if the ship has a length of about 170 m, rather long perhaps for many ships of this size for the design speed.

¹⁹ Most merchant ships have a service speed of about 15 knots, and if a length of 600 feet is assumed the ship is well below hump speed. Therefore, less horsepower is required to propel the ship. Less horsepower means smaller propulsion machinery, less fuel storage requirements, more cargo storage space, and therefore more chance to make money [Principles of Ship Performance. “Resistance and Powering of Ships” – Ch 07, pp. 7–23 web page: http://www.usna.edu/NAOE/courses/en200/ch07.pdf].

²⁰ The event that really brought about the escorting ‘boom’ was the catastrophic oil spill as a result of the grounding of the Exxon Valdez in 1989, Prince William Sound, Alaska and the Oil Pollution Act (OPA 90) that followed it.

²¹ As regards the tug types, see HENSEN, HENK. Tug Use in Port. A practical guide, The Nautical Institute, 2^nd edition 2003, London 2003, pp. 9 ff.

²² Azimuthing drives use conventional propellers in nozzles that can spin up to 360 degrees to provide thrust in any direction without a rudder and are commercialized by different manufacturers as Schottel, Aquamaster, Rolls-Royce, etc. Such a configuration is commonly known as “Z” drive. The name “Z-Drive” is derived from the drive shaft configuration which is horizontal off the engine, vertical through the hull, and horizontal at the propeller hub, thus forming a rough outline of a letter Z.

²³ In order to appreciate the distinctive features of an escort tug with azimuting Z drives propulsion using the escort towing methods see GALE, C. et al. “Perceived Advantages of Z-Drive Escort Tugs”, ITS'94. The 13^th International Tug & Salvage Convention and Exhibition (Southampton, UK). Complete papers and discussions, pp. 163–173, Thomas Reed Publications, Wiltshire, UK, 1994, and Optimised for escorting, Ship & Boat International, December 1994, pp. 12–17.

²⁴ The increased ship's resistance in shallow water paradoxically increases its minimum stopping distance. This reluctance to stop is because of the increase in the ship's apparent mass as it becomes more subjected to shallow water effects. It is known by naval architects as the “added mass” –the ship's virtual mass=its actual mass+the added mass– (see CLARK, I.C. Ship Dynamics for Mariners. The Nautical Institute, London 2005, p. 198). However, other authors think that it is more likely to be the water flow in the channel following the ship and filling the gap behind, which causes the delayed effect when a ship comes to an abrupt stop (see HENSEN, HENK. Tug Use in Port. A practical guide, The Nautical Institute, 2^a ed. London 2003, p. 81).

²⁵ There are cases, however, when external circumstances such as fire, explosions, etc., avoid fastening at the stern or remaining there, so that the only alternative is making fast at the bow of the tanker.

²⁶ See HENSEN, HENK. Tug Use in Port. A practical guide, The Nautical Institute, 2^nd. edition 2003, London 2003, pp. 46 ff.

²⁷ The angle at which a hydrofoil (in this case the rudder, or when the escort tractor Voith tug is using the indirect escort towing method, the entire underwater hull, especially the skeg) is inclined to the relative free stream water flow.

²⁸ It is the angle between the tanker's and the tug's centreline and in the escort towing slang, it is known as “hiking angle”.

²⁹ On an ASD tug, these maximum values will be on an angle of attack of about 50° and 70° respectively.

³⁰ See for example HENSEN, HENK. Tug Use in Port. A practical guide, The Nautical Institute, 2nd. edition 2003, London 2003, pp. 147 ff; SLOUGH, S.W., BROOKS, G. “Escorting Ships with Tractor Tugs”, Port Technology International, 11th edition, pp. 55–57, in p. 56; Safeguard of Tankers by Voith Water Tractors, by Voith Hydro Marine Technology, p. 5, web page: http://www.marcon.com/library/articles/2004/Safeguardtankers.pdf; and BARTELS, JENS-ERK, Comparative Considerations About the Funtion of a Voith Water Tractor and Pusher in the Indirect Mode, J.M. Voith GmbH, Ship Technical Division paper (unpublished), 8^th May 1992.

³¹ If the heel becomes excessive, the tug's Captain simply diminishes the propeller thrust; as a consequence, the angle of attack is reduced and the force decreases.

³² See for example the Det Norske Veritas -DNV- Rules for Ships 2005 edition Part 5 Chapter 7 Section 16: “Escort Vessels”.

³³ See Report of Results from Strait of Georgia Full-Scale Trials, p. 6, The Glosten Associates, Inc., April 1997 File No. 97022, web page: http://www.sfmx.org/support/tescort/acrobat/straitofgeorgiatrials.pdf.

³⁴ Nevertheless, this is the only method that was used with some limitations in USA by the conventional propulsion tugs working as escort tugs, using lines tight to the tanker's transom and passing through the tug's bullnose to provide steering forces (See Report of Results from Long Beach Full-Scale Trials, p. 6, The Glosten Associates, Inc., March 1997, File No. 97009, web page: http://www.sfmx.org/support/tescort/acrobat/longbeachtrials.pdf).

³⁵ See p. 6 of the report quoted on end note number 34.

³⁶ DNV -Det Norske Veritas- Rules for Ships 2005 edition Part 5 Chapter 7 Section 16 “Escort Vessels”.

³⁷ This is because the transverse metacentre M_T for this range of heel angles is a stationary point at the tug's centreline and in this case, the centre of buoyancy B moves in an arc whose centre is M_T. For heel angles higher than 10°, M_T moves off the centreline in a curved arc; the analysis of heels are made by means of a graph of the heeling angle versus the righting arm GZ that is called “Curve of Intact Statical Stability”. This graph lets it obtain the range of stability (i.e. the range of angles for which there is a righting moment, and therefore the range of heel where the tug exhibits an internal righting moment).

³⁸ It is the angle at which a hydrofoil –in this case the skeg– is inclined to the relative free stream of water flow.

³⁹ Other functions that are carried out by the skeg of a tractor Voith tug are the increasing of its directional stability when moving either bow or skeg first, and the improving of the “hydrofoil effect” of the entire hull when using it as an “active rudder” in the indirect escort towing method.

⁴⁰ Following the same reasoning, we could establish that in the case of an ASD escort tug, the bulbous bow is beneficial because this tug works bow first, and contrary to a tractor tug, the CLP should be as forward as possible, as a bulbous bow moves it in that direction. It is for this reason that since the first ASD escort tugs, most of them incorporate a bulbous bow to increase the lateral underwater area and to move the CLP forward. See in this sense GALE, C. et al. “Perceived Advantages of Z-Drive Escort Tugs”, ITS'94. The 13^th International Tug & Salvage Convention and Exhibition (Southampton, UK). Complete papers and discussions, pp. 163–173, Thomas Reed Publications, Wiltshire, UK, 1994, p. 171.

⁴¹ For example, the waves created will change the wet surface of the hull and the drag it experiences from viscous resistance.

⁴² For example see remarks by Dan Vyselaar from British Columbia University to the article Bray, Patrick J. “The bulbous bow. What is it, and why?” web page http://www.dieselduck.ca/library/articles/bulbous_bows.htm where he rejects two considerations from the author:

• —

  — “the increased sea keeping ability due to dampening of the pitching motion”.

• —

  — “the water coursing over the top of the bulb is exerting a downward pressure that is keeping the stern from squatting, thereby allowing flatter trim, causing the vessel to run with less resistance”.

⁴³ Rem, A., “Basic Aspects of Manoeuvring and Course keeping”. Training Course Hydrodynamics in Ship Design”. MARIN, November 1992.

⁴⁴ Pérez Rojas, L. et al, “El efecto del bulbo de proa en el comportamiento del buque en la mar (trabajos experimentales)”. OCEAN 2000, Valdivia (Chile), October 25–27^th (available online at http://canal.etsin.upm.es/publicaciones/OCEAN2000_final.pdf).